Duality without constraint qualification in nonsmooth optimization.
Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...
Dubins' problem is intrinsically three-dimensional
Dubins' problem is intrinsically three-dimensional
In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the...
Dykstra's algorithm as the nonlinear extension of Bregman's optimization method.
Dynamic contact problems with velocity conditions
We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems...
Dynamic coverage control design of multi-agent systems under ellipse sensing regions
This paper studies the dynamic coverage control problem for cooperative region reconnaissance where a group of agents are required to reconnoitre a given region. The main challenge of this problem is that the sensing region of each agent is an ellipse. This modeling results in asymmetric(directed) interactions among agents. First, the region reconnaissance is formulated as a coverage problem, where each point in the given region should be surveyed until a preset level is achieved. Then, a coverage...
Dynamic family of multicommodity inventory problems.
Dynamic MRR function optimization using calculus of variations.
Dynamic optimal cooling control for continuous casting of steel
Dynamic portfolio optimization with risk management and strategy constraints
We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution,...
Dynamic Programming: an overview
Dynamic programming as optimal path problem in weighted digraphs.
Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching
We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption...
Dynamic programming for stochastic target problems and geometric flows
Dynamic programming for the stochastic Navier-Stokes equations
Dynamic Programming for the stochastic Navier-Stokes equations
We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.
Dynamic programming in constrained Markov decision processes
Dynamic programming principle for stochastic recursive optimal control problem with delayed systems
In this paper, we study one kind of stochastic recursive optimal control problem for the systems described by stochastic differential equations with delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of optimal control problems and show that the value function is the viscosity solution of the corresponding infinite dimensional...
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...